The sub-supersolution method and extremal solutions of quasilinear elliptic equations in Orlicz-Sobolev spaces
type: Item
instance of: scholarly article
title: The sub-supersolution method and extremal solutions of quasilinear elliptic equations in Orlicz-Sobolev spaces
zbMATH Open document ID: 1400.35123
DOI: 10.1155/2018/8104901
author: Ge Dong
author: Xiaochun Fang
published in: Journal of Function Spaces
publication date: 2018-09-06T00:00:00Z
review text: Summary: We prove the existence of extremal solutions of the following quasilinear elliptic problem \(- \sum_{i = 1}^N (\partial / \partial x_i) a_i(x, u(x), D u(x)) + g(x, u(x), D u(x)) = 0\) under Dirichlet boundary condition in Orlicz-Sobolev spaces \(W_0^1 L_M(\Omega)\) and give the enclosure of solutions. The differential part is driven by a Leray-Lions operator in Orlicz-Sobolev spaces, while the nonlinear term \(g : \Omega \times \mathbb{R} \times \mathbb{R}^N \rightarrow \mathbb{R}\) is a Carathéodory function satisfying a growth condition. Our approach relies on the method of linear functional analysis theory and the sub-supersolution method.
Mathematics Subject Classification ID: 35J62
Mathematics Subject Classification ID: 35J25
Mathematics Subject Classification ID: 46E30
zbMATH DE Number: 6933358
zbMATH Keywords: quasilinear elliptic equation
zbMATH Keywords: Dirichlet condition
zbMATH Keywords: Orlicz-Sobolev spaces
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1155/2018/8104901
OpenAlex ID: W2886905933
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description: scientific article; zbMATH DE number 6933358